A computer's memory chip

jones_90

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Oct 1, 2012
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A computer's memory chip takes 166.6 ps to read/write data per cycle. What is the clock frequency of the memory?
 


We won't do your homework for you, but we will show you what is going on. I'll give a similar example but with different numbers to explain.

What you want to do is to find out how many read/write cycles per second the chip can perform. This requires dimensional analysis where you multiply out the unit conversions to eventually get your results.

A chip with a 500 ps cycle time has 1 cycle per 500 ps. One picosecond is 10^-12 sec. So:

1 cycle / 500 ps * 1 ps / 10^12 sec. Cross multiply (sorry there is no LaTex or OpenOffice Math type pretty print here) and cross out like terms appearing on both sides of the divisor bar and you get:

1 cycle / 500 * 1/10^-12 sec. Multiply that through and get 1 cycle/500 * 1/10^-12 sec = 2x10^9 cycle/sec.

1 Hz is 1 cycle/sec so multiply our answer by that:

2x10^9 cycles/1 sec * 1 Hz/cycle/sec. Seconds is under two denominators so comes to the top: 2x10^9 cycles/1 sec * (1 Hz*sec)/cycle. Multiply through and cancel:

2x10^9 cycles/1 sec * (1 Hz*sec)/cycle = 2x10^9/1 sec * 1 Hz*sec = 2x10^9 * 1 Hz = 2x10^9 Hz. Your 500 ns chip runs at 2x10^9 Hz. 1x10^9 Hz = 1 GHz so we have a 2 GHz part.

Hope that is clear for you.